Regularized Wasserstein Means for Aligning Distributional Data
This work addresses alignment challenges in distributional data for domains such as machine learning and computer vision, though it appears incremental as it builds on existing Wasserstein mean methods.
The authors tackled the problem of aligning distributional data by proposing regularized Wasserstein means, which resulted in a sparse representation that reduces mapping cost and demonstrates scalability and robustness in applications like domain adaptation and point set registration.
We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the variational transportation to distribute a sparse discrete measure into the target domain. The resulting sparse representation well captures the desired property of the domain while reducing the mapping cost. We demonstrate the scalability and robustness of our method with examples in domain adaptation, point set registration, and skeleton layout.